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Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback

M’Closkey, Robert T. and Murray, Richard M. (1994) Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback. In: Proceedings of 1994 33rd IEEE Conference on Decision and Control. Vol.2. IEEE , Piscataway, NJ, pp. 1317-1322. https://resolver.caltech.edu/CaltechAUTHORS:20190318-130817404

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Abstract

This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The stability is defined with respect to a nonstandard dilation and is termed "δ-exponential" stability. The δ-exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm (1992) for smooth feedbacks. Converse Lyapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.1994.411139DOIArticle
ORCID:
AuthorORCID
M’Closkey, Robert T.0000-0003-1443-8217
Murray, Richard M.0000-0002-5785-7481
Additional Information:© 1994 IEEE. Supported in part by AFOSR F49620-92J-0293. Supported in part by a grant from the Powell Foundation.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-92J-0293
Charles Lee Powell FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20190318-130817404
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190318-130817404
Official Citation:R. T. M'Closkey and R. M. Murray, "Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback," Proceedings of 1994 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA, 1994, pp. 1317-1322 vol.2. doi: 10.1109/CDC.1994.411139
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93927
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Mar 2019 20:24
Last Modified:03 Oct 2019 20:59

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